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Here is how I am plotting the three implicit functions:

  Show [ ContourPlot[f[h, a] == 0, {a, 0, 0.6}, {h, 0, 1}, 
         ContourStyle -> Black], 
         ContourPlot[f2[h, a] == 0, {a, 0, 0.6}, {h, 0, 1}, 
         ContourStyle -> Red], 
         ContourPlot[f3[h, a] == 0, {a, 0, 0.6}, {h, 0, 1}, 
         ContourStyle -> Blue] ]

This works fine but I would like to add a legend, axis labels, larger fonts for the axes etc. I am using Mathematica 11.

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    $\begingroup$ To come up with an answer, most of us would want to run tests with your code. But you give us code with undefined symbols that won't evaluate. I think you are likely to get an answer if you would edit your question to include *all the code needed to reproduce your problem. $\endgroup$
    – m_goldberg
    Oct 12 '19 at 23:31
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Arbitrary functions:

f[h_, a_] := h^2 - a^2

f2[h_, a_] := 2 h^2 - a^3

f3[h_, a_] := h^2 - 2 a^2

A single ContourPlot can handle multiple functions. This makes adding PlotLegends and other shared options quite easy.

ContourPlot[
 {f[h, a] == 0, f2[h, a] == 0, f3[h, a] == 0},
 {a, 0, 0.6}, {h, 0, 1},
 PlotLegends -> Placed["Expressions", {0.25, 0.7}],
 FrameLabel -> Automatic,
 BaseStyle -> {FontSize -> 14}]

enter image description here

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