Who do you pay taxes to if you travel a lot?

Consult your digital accountant.

Where you home is.

States and countries impose taxes on individuals and businesses for the privilege of doing business in that state or country (this includes work as an employee). You owe tax to the state or country in which you conduct business. Most states or countries also have tax credits for tax paid to another state or a foreign tax credit.

For example, if you are a US citizen, you must report all of your worldwide income to the IRS. There is a foreign tax credit that is based on taxes you paid to foreign countries. You have to complete all the tax returns for the other country or state before you can complete the return for your home state or country.

Multi-country taxation is about as complicated as you can get when it comes to successfully navigating tax laws. Don't be an idiot and think you can file your own returns if you're working out of the country. Hire a competent tax professional who has experience with multi-dimensional tax situations.

you need a 'home' country, with a passport also... where your primary residence is would normally be who you pay taxes and such to

The one you are a citizen of.