I couldn't find a breakdown of registration by party for Harris County. Maybe they don't do it that way in Texas.
In 2016, Republican voters outnumbered Democratic voters 3:2 in Harrison County.
Trump, Clinton, and Sanders are from New York City (Youtube)
I'm pretty sure that Ted Cruz is not a native of the Lone Star State. I read somewhere that he is a native of the great state of Canada. Perhaps that was your point. 
jimrtex, so every one is unaffiliated until he votes? Okay, that would explain why it wasn't easy to find party registrations in Harris County. I did see somewhere that in 2012 Romney voters outnumbered Obama voters. In fact, Dave Leip's US Election Atlas has that info. I actually like that situation. In Pennsylvania, you have to pick a party and pick it early. Four weeks before the primary election, or something like that. On the other side of the spectrum is Iowa, where there's same-day registration. I lived in Iowa for five years. There, you can decide whether you're a Democrat or a Republican or a Libertarian or a Socialists or whatever on the day of the caucus. Of course, the day of the caucus is in early January and it's usually a day when the high temperature is about 20 degrees Farhenheit and there is about two feet of snow outside, and you have to show up early for a good parking spot and stay there for many hours. I guess ou can't have everything.
Historically, primaries in Texas were conducted by the political parties, and in a legal sense, they still are. They are also conducted by county political parties, so that if a party is not organized in a county, there is no primary in that county. Political parties also conduct party conventions, with a hierarchical system like in Iowa - precinct, county, and state. The precinct conventions are held on primary election night. Until about the mid-20th century, the Republicans rarely had primaries (the most successful parties must have primaries; medium successful parties have a choice between primaries or conventions; and small and new parties nominate by convention). Texas currently has four parties, the Republicans and Democrats nominate by primary, while the Libertarian and Greens nominate by convention.
Back in the day, the Democratic primary was held on a Saturday (in July or August), and after the votes were counted, the precinct convention would commence. Since there was effectively only one party, it was typical for more votes to be cast in the primary than the general election. If no candidate had a majority in the primary, it would be decided in the runoff. A runoff was quite normal for important races such as governor, since challengers weren't really running against the party standard-bearer but rather simply a previous winner.
Because the party was paying for the primary, they would want to control costs, so they would use paper ballots, and the election workers would be volunteering their time for their party. If there were two primaries, they had different polling places. If they were in the same building, it would be preferred that they had separate outside entrances. If there are signs identifying the entrances, either both had to have a party name or symbol, or neither had a party name or symbol.
The restriction on participation is that you can only participate in the nominating activities of one party. The pledge on the ballot doesn't say anything about political fealty, but only that you had not, and will not participate in the nominating activities of another party.
Primaries use a parallel structure without direct involvement of the state or county government. Filing is with either the state party chair or county party chair (independents file with the SOS or county clerk). The state party chair then informs the county party chairs of the candidates for statewide or district election so that the county chairs can prepare ballots. The county party would hold the primary, canvass the results. The county party then informs the county clerk who the party nominated for the general election. They would also pass their canvass on to the state party, which would conduct the statewide canvass, and then inform the SOS who they nominated. The parties would also determine if they had to have a runoff primary or not, which are only held in areas where there is an active race.
But in practice, there is more state and county involvement. The state pays for primaries, and county parties don't own voting machines, don't know how to program them, and don't know how to count votes. So they rent machines from the counties, who also programs them and count the votes. It used to be that the state would write a check to the county parties for the primary, who would in turn pay the counties. But after one party treasurer embezzled the money, the state now issues a voucher which the party gives to the county, who can then get the money from the state. In another county, the county chair disappeared (literally). There is a party account in a bank, that because of banking laws, can not even be determined if it has any money in it.
Early voting is also conducted by the counties, and most voters vote early. So the party chairs also tell the counties who to put on the ballot. When you vote early, you go to the polling place and state which party primary you wish to vote in. On election day, you would go to a party-specific polling place and vote. On election night, county parties are required to report results every 15 minutes to the SOS. This really isn't a burden, since the actual counting is being done by the county election officials who have the same reporting requirement on general election day.
Because Harris County is so evenly divided, and because there is straight-ticket voting there is a concern that if voters don't vote for Trump or Clinton that they will either not mark the straight ticket device or not continue to vote down ballot. There are 49 partisan offices on the general election ballot. A few percentage points either way will wipe out dozens of judges. This is likely the real reason for Cruz's endorsement of Trump.
