how do i stop messages from my iPhone from showing up on my laptop

Good day Scott,

It's good to see you contributing to Apple Support Communities by posting here. I hope we will continue to see more in the future.

It sounds as though you are getting Messages coming through both your iPhone and your Mac but want to get them only on the iPhone. Is that right?

The easiest way to eliminate this issue would be to sign out of the Apple ID being used for messaging on the iPhone. Go to Settings > Send & Receive > Select your Apple ID and Sign Out. Now all messaging traffic will use your phone number and thus will go only to the phone.

Alternatively you can disable to account on your Mac. In Messages go to the Messages menu > Preferences > Accounts > iMessage. Sign out of or disable to account.

Thanks for using Apple Support Communities.

Safe computing.

Open up Settings and then scroll down until you see Messages and tap on it. Then turn off Text Messages Forwarding.

Hi,

You have posted in Mavericks (OS X 10.9) which does not allow you to do the option Eric suggests.

However the set up is normally set Messages going on the iPhone.

This Registers the Number and iMessages can be sent to either Apple IDs registered for iMessages or any phone number as it will send texts if the person is not registered with iMessages.

On the Mac there is a Mac version with an iMessages account that you use and Apple ID for.

You can then add that Apple ID to the iPhone settings fro Send an Receive and the Mac and iPhone will sync iMessages whether addresses to the iPhone number or the Apple ID you are using.

As has been said you can restrict either of these on either version.

Or you an Sign Out of the Apple ID on the iPhone and deselect the iPhone number on the Mac (There is no way to delete the iPhone Numbers or other emails you might have added - you can only turn them Off - unless you dig around and remove the .plist and effectively Reset the iMessages account on the Mac).

In Yosemite and above there is the option Eric talks about about being able to Forward the Text (SMS) chats to the Mac.

The iPhone needs to be on the same Network as the Mac (your Home LAN).

The two versions need to be using the same Apple ID - so the set up I describe needs to be done.

You then set "Text Forwarding" on the iPhone. This causes a Code Number to appear on the Mac which you then enter back on the iPhone.

To cancel you just Unset Text Forwarding or take the iPhone off the LAN as Eric said.

The clue might be

... texts me on my iPhone, ...

which seems to be the bit Eric focused on.

It can be a case of semantics and you meant iMessages or all types of Messages that the iPhone can receive in the Messages app in which case Brett's answer will serve you better.

9:33 p.m. Tuesday; October 13, 2015