Stopping rain collecting
If the existing surface preparation is sloped the wrong direction and water runs to an undesirable area then you would normally work to re-install the surface preparation to get a different slope. 

Since you have a desire to not replace your tarmac due to cost considerations then your only real choice is to do one of the following:


Install an additional curbing at the lower edge of the tarmac area to divert the runoff water to another area. The height of curbing required would be fully dependent on conditions at your site.
Install a French style drain at the area adjacent to the tarmac. This drain would be a pit dug into the ground that can accept the run off water and allow it to disperse into the soil. Generally such pit is filled with rocks or course material that can let water enter easily into the pit. It is often good to cover the pit with a screen and lid. The screen can be used to filter organic material from entering the drain and hopefully preventing it from plugging up. 
You could install a sump pit with a water pump unit. The pit would have an opening at the low spot where water collects so that the water can enter the sump pit. A water level switch on the pump system turns on the pump when the a certain level of water has accumulated. The pump moves the water out of the sump pit through a drain pipe that is plumbed to an area where the water can be safely discharged. This could be to a lower area of your property, out to the street curb or into a storm sewer system. This solution also requires the availability of electrical service to the pump area.